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Credit Freezes, Equilibrium Multiplicity, and Optimal Bailouts in Financial Networks

Author

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  • Matthew O. Jackson
  • Agathe Pernoud
Abstract
We analyze how interdependencies between organizations in financial networks can lead to multiple possible equilibrium outcomes. A multiplicity arises if and only if there exists a certain type of dependency cycle in the network that allows for self-fulfilling chains of defaults. We provide necessary and sufficient conditions for banks' solvency in any equilibrium. Building on these conditions, we characterize the minimum bailout payments needed to ensure systemic solvency, as well as how solvency can be ensured by guaranteeing a specific set of debt payments. Bailout injections needed to eliminate self-fulfilling cycles of defaults (credit freezes) are fully recoverable, while those needed to prevent cascading defaults outside of cycles are not. We show that the minimum bailout problem is computationally hard, but provide an upper bound on optimal payments and show that the problem has intuitive solutions in specific network structures such as those with disjoint cycles or a core-periphery structure.

Suggested Citation

  • Matthew O. Jackson & Agathe Pernoud, 2020. "Credit Freezes, Equilibrium Multiplicity, and Optimal Bailouts in Financial Networks," Papers 2012.12861, arXiv.org, revised Jul 2023.
    • Handle: RePEc:arx:papers:2012.12861
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    References listed on IDEAS

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    Cited by:

    1. Csoka, Peter & Herings, P.J.J., 2022. "Centralized Clearing Mechanisms in Financial Networks : A Programming Approach," Discussion Paper 2022-008, Tilburg University, Center for Economic Research.
    2. Csóka, Péter & Herings, P. Jean-Jacques, 2021. "Uniqueness of Clearing Payment Matrices in Financial Networks," Research Memorandum 014, Maastricht University, Graduate School of Business and Economics (GSBE).
    3. Hamed Amini & Zhongyuan Cao & Agnes Sulem, 2021. "Limit Theorems for Default Contagion and Systemic Risk," Papers 2104.00248, arXiv.org.
    4. Chien-Hsiang Yeh, 2022. "Uniqueness of Equilibria in Interactive Networks," Papers 2206.00158, arXiv.org.

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    More about this item

    JEL classification:

    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation
    • G38 - Financial Economics - - Corporate Finance and Governance - - - Government Policy and Regulation

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